The halo merger rate in the Millennium Simulation and implications for observed galaxy merger fractions

We developed a new method to extract halo merger rates from the Millennium Simulation. First, by removing superfluous mergers that are artifacts of the FOF halo finder, we find a lower merger rate compared to previous work. The reductions are more significant at lower redshifts, lower halo masses, and minor mergers. Our approach agrees better with predictions from the EPS model. Second, we find that the FOF halo finder overestimates the halo mass by up to 50% for halos that are about to merge, which leads to an additional ~20% overestimate of the merger rate. Therefore, we define halo masses by including only gravitationally bound particles. We provide new best-fitting parameters for a global formula to account for these improvements. In addition, we extract the merger rate per progenitor halo, as well as per descendant halo. The former is the quantity that is related to observed galaxy merger fractions when they are measured via pair counting. At low mass/redshift the merger rate increases with mass and redshift. At high mass/redshift (for halos with masses a few times the "knee" of the mass function) these trends break down, and the merger rate per progenitor halo decreases with mass and increases only moderately with redshift. Defining the merger rate per progenitor halo also allows us to quantify the rate at which halos are being accreted onto larger halos. We provide an analytic formula to convert given merger rates per descendant halo into merger rates per progenitor halo. Finally, we perform a comparison between observed merger fractions and the fraction of halos that have undergone a major merger during the recent dynamical friction time, and find a fair agreement, within the large uncertainties of the observations. Our new halo merger trees are available at http://www.mpe.mpg.de/ir/MillenniumMergerTrees/.